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arXiv · 2312.11773

Compatible Decomposition of the Casselman Algebra and the Reduced Group C*-algebra of a Real Reductive Group

Jacob Bradd
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Abstract

For a real reductive group $G$, we investigate the structure of the Casselman algebra $\mathcal{S}(G)$ and its similarities to the structure of the reduced group $C^*$-algebra $C_r^*(G)$. We demonstrate that the two algebras are assembled from very similar elementary components in a compatible way. In particular, we prove that the two algebras have the same $K$-theory when restricted to a finite set of $K$-types, which is a refinement of the Connes-Kasparov isomorphism.

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BibTeXRIS

Jacob Bradd. 2023-12-19. Compatible Decomposition of the Casselman Algebra and the Reduced Group C*-algebra of a Real Reductive Group. https://arxiv.org/abs/2312.11773

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